MAT 682 
Advanced Topics in Differential Geometry 
Fall 2003 
TuTh 2:20-3:40, Physics P-128 

Prof. Claude LeBrun.
Office hours:
TuTh 1:00--2:00, Math Tower 3-108.

Riemannian Manifolds of Special Holonomy

This course will discuss the construction of compact Riemannian manifolds with non-trivial parallel tensor fields. These manifolds are interesting for many different reasons, but one important motivation for studying them is that they typically turn out to be Einstein.

After a brif introduction to Riemannian holonomy, we will give a self-contained treatment of the theory of Calabi-Yau and hyper-Kähler manifolds. We will then focus on Joyce's construction of manifolds of holonomy G2 and Spin(7).

Prerequisite: MAT 569, or permission of the professor.

Grades will be based upon class participation.

The Professor may be reach by e-mail at

 This is the best method for making appointments outside normal office hours.

DSS advisory. If you have a physical, psychiatric, medical, or learning disability that could adversely affect your ability to carry out assigned course work, please contact the Disabled Student Services office (DSS), Educational Communications Center (ECC) Building, room 128, (631) 632-6748.  DSS will review your situation and determine, with you, what accommodations are necessary and appropriate. All information and documentation regarding disabilities will be treated as strictly confidential.

Students for whom special evacuation procedures might be necessary in the event of an emergency are encouraged to discuss their needs with both the instructor and with DSS. Important information regarding these issues can also be found at the following web site: